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Saving Gammon |
Advanced Gammon Avoidance
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| From Backgammon Times, Volume 3, Number 3, Fall 1983. |
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| Bob Floyd |
When analyzing a gammon-avoidance position, you should first try to estimate how likely the gammon is. Your correct play depends very much on whether you can be optimistic or not. Estimate how many rolls it will take your opponent to bear off. To avoid being gammoned, you must take a checker off in one roll fewer. If you expect your opponent to be off in four rolls, you will have three. You can reasonably expect to do so if you need no more than five outside crossovers, and about twenty as an outside pip count. With more than five crossovers, you must depend on rolling a double; with exactly five, you must depend on not missing a subsequent crossover.
If either the pip count or the crossover count dictates pessimism, you must plan to use large doubles effectively. However, except for one-roll situations, this is seldom best done by stacking your checkers on one point; you should be sure that average rolls play well while you wait for the saving 5-5.
If the counts allow optimism, you should take precautions against rolling small numbers; if you expect to have three more turns, for example, and you will need four outside crossovers, try to play so that you will not miss every time you roll an ace; otherwise even rolling 1-6 twice will destroy you.
In intermediate situations, you must balance many conflicting needs. You should try to make crossovers where possible, but you should also try to protect yourself against rolling specific bad numbers (normally 1s) or never rolling a specific needed number (usually a 6), and you should try not to waste pips inside your home board because wasted pips return to haunt you as later missed crossovers. As a general rule, you should consider wasting pips to get down to an odd number of outside crossovers, but not to an even number; there are exceptions, though. Most of the positions that follow are intermediate-to-optimistic; they call for subtle play to guard against certain unobvious dangers.
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Position A. Black to play a 2. |
Here, only the first danger is present. The needed pip count is only eight or nine, easy to roll in two turns. I looked at rolls containing ones. The play of 9/7 looked safe even if both numbers contained a one. The first roll could be played 7/6, 9/?; the second, 7/6, ?/off. Only 1-2 seemed to offer difficulties. The play of 7/5, if followed by any ace, would leave Black with a checker on the 8 or 9 point and a gap on the ace point, so that another ace would miss again. We played 9/7, and sighed in relief when our next roll was 6-1. We had only two bad rolls (1-2 and 2-1) to worry about, rather than eleven. Later, I looked at every two-roll sequence in this position; there is no sequence that would have made us regret playing 9/7, while any of 1-1, 1-3, 1-4, 1-5, and 1-6 followed by another number of this same set misses if we play 7/5.
The moral: when you are a favorite to escape the gammon, look at your worst rolls, especially those containing aces. If you don't have several checkers which can cross over with aces, you are at risk of missing a crossover. If you also have no checkers on the 2, 8, 14, and 20 points, as in position A, you run the risk of missing twice in a row on rolls containing aces.
At the other end of the spectrum, some positions will miss unless you roll one or more sixes, even though the total pip count is modest.
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Position B. Black to play 3-2. |
Position C, from Magriel's Backgammon, pg. 79, is a close analogue of Position B.
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Position C. Black to play 4-2. |
Position D is also from Magriel, pg. 80, and is also misplayed there.
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Position D. Black to play 5-2. |
When you come down to one last outside checker and you have not slotted the one point, you may have one of these positions:
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If the outside checker is on the 8 or 9 point, you will wish you had played 2/1. If it is one the 11 or 12 point, you will be glad you didn't. On the 7 or 10 point, it makes no difference. Until you can predict where the last checker is likely to be, hold off on slotting inside points. Position F (from Deyong's Playboy's Book of Backgammon, Diagram 5-15) exemplifies this.
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Position F. Black to play a 1. |
When there is a single outside checker, it is occasionally right to slot the ace point before the next-to-last roll.
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Position G. Black to play a 1. |
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Position H. Black to play 3-3. |
To bring in none or one of the checkers on the 8-point leaves too many crossovers, unless X rolls another doubles. To bring two in and play 18/12 creates the double dangers of rolling a 1 on the next roll and of not rolling a six in the next two rolls. So the candidate plays are to bring in 3 or 4, resulting in positions H3 and H4.
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If the numbers on the next roll total nine or more, Black is virtually sure to be off on the following roll, in either position. If the numbers total less than six, they require a subsequent double, except for 3-2. We need only look in detail at the remaining numbers:
The preponderance favors H3, although they are close. The most important decision, though, is to reject bringing in just two checkers.
In a longer race to get off the gammon, it becomes important to know whether or not you are favored. Usually in these situations you can count pairs of checkers as rolls for your opponent, and pairs of crossovers or eights of pips (whichever is larger) as rolls for you. If you are favored, it becomes most important to follow traditional principles: diversify in your outfield; don't waste pips; take crossovers; bear in to your six-point. If you are significantly behind, plan to take advantage of large numbers and especially the large doublets; play your outside checkers to the 18, 16, 12, and 11 points. If the race is fairly even, correct play depends on whether you are pip-count bound or crossover bound.
If pip-count bound, assume that to have a chance you must roll 4's, 5's, and 6's anyway, so place checkers on the high points of your outfield. If crossover bound, avoid creating positions where too many aces or not enough sixes will hurt you. Either way, in most races where you have a medium chance, desperation plays of stacking several checkers on a single point or bearing deep into your home board are very suspect. Remember, when you are tempted to waste pips to save a crossover, a bad pip count can be expected to turn into missed crossovers later.
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Position I. Black to play a 3. |
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Position J. Black to play a 3. |
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Position K. Black to play a 1. |
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Position L. Black to play a 1. |
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Position M. Black to play a 1. |
The gains from each play are these combinations:
| Play | First Roll | Second Roll | Total (in 1296) |
| 12/11 | 5-2, 5-3 5-4 4-4 5-5 |
4-4, 5-5 3-3, 4-4, 5-5 5-1, 5-2, 5-3, 5-4 twenty-one rolls |
43 |
| 10/9 | 6-2, 6-3 3-3 |
3-3 6-1, 6-2, 6-3, 6-4, 6-5 |
14 |
| 8/7 | 1-6 1-1, 1-3, 1-4 |
4-4, 5-5, 6-6 6-6 |
13 |
Notice that Black gains more (14 chances in 1296) on 12/11 by not missing on an initial 5-2, 5-3, or 5-4 than he does on 8/7 by rolling a 3-3 (only 10 in 1296).
The moral: even when your position is desperate, if there is more than one roll remaining you should prepare for normal rolls rather than for a specific doubleton.
| More articles by Bob Floyd |
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| More articles on saving gammon |
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Return to: Backgammon Galore |
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